Braid group statistics implies scattering in three-dimensional local quantum physics

TL;DR

This paper demonstrates that particles with braid group statistics in three-dimensional quantum physics must undergo elastic scattering in all directions and energies, implying they cannot be free and challenging the existence of certain localized operators.

Contribution

It proves that braid group statistics particles cannot be free and must scatter elastically, extending previous no-go theorems and analyzing the implications for localized operators.

Findings

Particles with braid group statistics cannot be free.

Elastic two-particle scattering occurs in all directions and energies.

Trivial 2-particle S-matrix if no scattering in a small solid angle.

Abstract

It is shown that particles with braid group statistics (Plektons) in three-dimensional space-time cannot be free, in a quite elementary sense: They must exhibit elastic two-particle scattering into every solid angle, and at every energy. This also implies that for such particles there cannot be any operators localized in wedge regions which create only single particle states from the vacuum and which are well-behaved under the space-time translations (so-called temperate polarization-free generators). These results considerably strengthen an earlier "NoGo-theorem for 'free' relativistic Anyons". As a by-product we extend a fact which is well-known in quantum field theory to the case of topological charges (i.e., charges localized in space-like cones) in d>3, namely: If there is no elastic two-particle scattering into some arbitrarily small open solid angle element, then the 2-particle S-matrix is trivial.